Public-key encryption is a field of cryptography using two separate keys, one of which is secret (private) and one of which is called public. Although different, the two parts of the key pair are mathematically linked. One key locks or encrypts the plaintext to obtain cipher text, and the other unlocks or decrypts the cipher text to obtain the plaintext again. The public key cannot perform the decryption function without the private key. The public key may even be published, and yet an attacker is not helped in decrypting cipher texts. Public-key encryption is also known as asymmetric encryption.
The known algorithms used for public key cryptography are based on mathematical relationships such as the integer factorization and discrete logarithm problems. Although it is computationally easy for the intended recipient to generate the public and private keys, to decrypt the message using the private key, and easy for the sender to encrypt the message using the public key, it is difficult for anyone to derive the private key, based only on their knowledge of the public key. The latter differs from symmetric encryption, in which decryption keys either equal their corresponding encryption key or are easily derived therefrom.
Public-key cryptography is widely used. It is an approach used by many cryptographic algorithms and cryptosystems.
The problems on which known public-key encryption system are based are resource intensive. For example, RSA encryption, which is a known public-key encryption system, requires for key generation, that two large prime number p and q are generated. Decryption requires exponentiation on similar sized numbers.
Reference is made to the article “Key Exchange and Encryption Schemes Based on Non-commutative Skew Polynomials” by Delphine Boucher, et al. The article relates to a key exchange algorithm based on so-called non-commutative skew polynomials.
Reference is further made to the article “Key Agreement Protocols Based on Multivariate Polynomials over Fq” by Yagisawa Masahiro. The article relates to key agreement protocols based on multivariate polynomials that are not evaluated.